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Question

Difficulty: EasyDivisibility, Factors, and Multiples

What is the smallest positive integer greater than 11 that leaves a remainder of 11 when divided by each of 44, 66, and 88?

Answer: 25

Answer

The correct answer is 25.
The least common multiple of 4, 6, and 8 is 24, which is the smallest positive integer divisible by all three numbers. To leave a remainder of 1 upon division by each, we add 1 to 24, resulting in 25.

Step-by-Step Solution

1
Calculate the least common multiple (LCM) of 4, 6, and 8.
\text{LCM}(4, 6, 8) = 24
Any positive integer divisible by 4, 6, and 8 must be a multiple of their least common multiple.
2
Add the desired remainder of 1 to the LCM.
24 + 1 = 25
Adding 1 to a common multiple guarantees that division by 4, 6, or 8 yields a remainder of 1.

Key Concept

Least Common Multiple (LCM) and Remainder Properties
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Topics

Divisibility, Factors, and Multiples

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